Interacting Particle Systems with Rapid Stirring
The research deals with a continuous time contact process on the lattice ?^? for ?>2. The model describes the behavior of particles performing branching on the lattice in the presence of rapid stirring, that is, a pair of particles with certain distance exchange at a high rate. In addition to stirring, each particle dies or splits at certain rates. In the case of splitting, the newborn particle is sent to another site in according to a certain distribution; if the newborn lands on an occupied site, its birth is suppressed. The process is also known as contact process combined with an exclusion process. The aim is to study the long time behavior of the system, in particular, finding asymptotic behavior of the probability of survival as the rate of stirring approaches infinity.